1. What is 2y(t) in Laplace domain?
Incorrect. The impulse function 2δ(t) is from the inverse Laplace transform of the number 2
Correct. The Laplace transform of a time domain variable y(t) is the same variable but in the Laplace domain Y(s).
Incorrect. Laplace domain (s) and time domain (t) functions never appear together
Incorrect. The conversion to Laplace domain is not integration
2. What is the Laplace transform of d2fdt2 with f(0) = 1 and f'(0) = 2?
Incorrect. The solution is s2F(s)-sf(0)-f′(0)
Incorrect. The solution is s2F(s)-sf(0)-f′(0)
Correct. The solution is s2F(s)-sf(0)-f′(0)
Incorrect. The sign before the f'(0) should be negative
3. What is the initial and final value of Y(s) = (s+3)s(2s+5)(3s+6)?
A. Initial: 1, Final: 1/10
Incorrect. Use IVT: y0=lims→∞sY(s) and FVT: y∞=lims→0sY(s)
Incorrect. Use IVT: y0=lims→∞sY(s) and FVT: y∞=lims→0sY(s)
Incorrect. Use IVT: y0=lims→∞sY(s) and FVT: y∞=lims→0sY(s)
D. Initial: 0, Final: 1/10
Correct.
IVT: y0=lims→∞sY(s)=∞+3(2⋅∞+5)(3⋅∞+6)=0
FVT: y∞=lims→0sY(s)=3(5)(6)=110